1. Field of the Invention
This invention relates generally to thermal radiation analysis. More specifically this invention relates to radiometric determination of temperature, emissivity, and stray light.
2. General Background and Description of Related Art
Optical pyrometers are of three general types: brightness, ratio, or multiwavelength (i.e. MW). Brightness and ratio pyrometers require prior knowledge of surface emissivity and environmental interference. In addition to wavelength, emissivity, which is the ratio of the emitted radiation of a real radiator to that of an ideal one, can depend on composition, surface finish, and temperature. Environmental interference in the form of radiation absorption or scattering within the transmission medium can also be a problem.
Brightness devices rely on capturing a known fraction of the energy emitted by the target; the user must know the emissivity to get the correct temperature value. For many circumstances this may not be possible.
Ratio pyrometry attempts to circumvent the emissivity issue by utilizing the ratio of the intensities measured at two different wavelengths instead of the intensity magnitude. The resulting representative equation is solved for temperature with the assumption that the division has canceled out the emissivity. This method works if the emissivity is the same at both wavelengths, but this is only certain in an ideal or semi-ideal (gray-body) radiator. Concern over emissivity cancellation affects the design of ratio pyrometers: the closer together the wavelengths are chosen, the more likely the emissivities are to cancel, but the greater the degradation of actual performance. As a result, accurate temperature measurements with this approach is not possible in many instances. One way to minimize the errors is to average the results of many ratio pairs (Felice, U.S. Pat. No. 5,772,323); however, this approach cannot calculate accurate source temperatures for functional forms of the emissivity that systematically increase or decrease the color temperature.
Multiwavelength (MW) pyrometry was developed to simultaneously calculate the temperature and spectral emissivity of a thermal radiator from spectral intensity measurements made at several wavelengths. Originally, this involved assuming a specific parameterized wavelength dependence of the spectral emissivity, and utilizing spectral intensity measurement data to determine the adjustable parameters by solving simultaneous equations involving the Plank distribution for the parameters and the temperature. However, this method is highly sensitive to radiation intensity measurement errors and to differences between the actual and assumed emissivity functional forms, which increase the temperature calculation errors as the number of parameters increase.
A subsequent MW approach provides an improvement to the original approach by determining the temperature and emissivity parameters using best-fit least-squares fitting of numerous spectral intensity data points (Kahn, et al., U.S. Pat. No. 5,132,922). This reduces the sensitivity to measurement errors by removing the emphasis from an exact functional fitting of the experimental data. Instead, the regression fit utilizes the statistical averaging of a large data set to more accurately determine temperature. An additional improvement is to preprocess the measurement data to minimize the effects of noise and external influences before utilizing the curve fitting technique. However, even these improvements do not prevent significant errors for a variety of functional forms of the emissivity.
The main problems with current MW approaches include the following:
1. The assumed functional forms of the emissivity distribution may not adequately describe the wavelength dependence and lead to significant errors in the temperature computation.
2. Unaccounted for spectral components of reflected or transmitted stray light can severely limit measurement accuracy.
3. Measurements within media that absorb and radiate can significantly degrade calculations.
The invention provides new types of thermal radiation analysis and analyzers that determine temperature and can be used to determine spectral emissivity, the spectral distribution of extraneous radiation and atmospheric absorptivity as well. It comprises a two-stage, passive MW measurement approach, each stage of which is novel. Neither stage requires prior knowledge or independent assessment of the emissivity, and the final calculated temperature and emissivity are insensitive to the functional form of the emissivity. Stage-1 provides an emissivity compensating methodology that typically provides accuracies of less than 1%, and Stage-2 provides a multi-temperature simultaneous calculation that utilizes the results of Stage-1 to provide typical accuracies of less than 0.1 K.
For a thermal radiation source at temperature T, the following approximate relationship can be written for the measured spectral intensity W(xcex,T), and the emissivity xcex5(xcex,T),
Ln[W(xcex,T)xcex5xcex1]xe2x88x92Ln[xcex5(xcex,T)]=xe2x88x92a0/(xcexT)xe2x80x83xe2x80x83(1)
xcex1 is a constant that depends on the solid angle of light intercepted (xcex1=37415, for xcex in units of microns and W in units of Watts/m2, when all the radiated light is intercepted), xcex is the wavelength, Ln is the natural log, and a0 is a constant equal to 14388 xcexcmK (xcex in units of xcexcm and T in units of K). The idea is provide a best fit of the right-hand-side (RHS) of Eqn. (1) to the left-hand-side (LHS) to determine T. Unfortunately, xcex5(xcex,T) is generally unknown; however, the spectral variation of the emissivity term is much less than that of the spectral intensity term, and a rough estimate of the emissivity term is enough to provide a fairly accurate estimate of T. Initially, the emissivity term is assumed to be constant, and a spectral least squares best-fit of the RHS and the emissivity term to the intensity data in Eqn. (1) is used to determine T and the constant emissivity within various spectral sub-regions (approximately 10 contiguous sub-regions) of W(xcex,T) such that the LHS best fits the RHS, thereby determining if the color temperature is generally increasing, decreasing, or remaining constant with wavelength. Then, an emissivity of a predetermined functional form that yields a similar increase, decrease or constant color temperature is determined, and a new value for T is calculated using Eqn. (1). More explicitly, Ln[xcex5(xcex,T)] can be written as,
Ln[xcex5(xcex,T)]=x0(T)+x1(xcex,T)xe2x80x83xe2x80x83(2)
The simplest approximation for x1 is,
x1(xcex,T)=sx(T)(xcexxe2x88x92xcexL)xe2x80x83xe2x80x83(3)
xcexL is the shortest wavelength of the measured spectrum. sx is determined by choosing the value that best reproduces the changes in color temperature observed. More explicitly, by inserting Eqn. (2) and Eqn. (3) into Eqn. (1) and solving for sx if there is an equal number of wavelengths in the different sub-regions, then for the jth wavelength in the ith subregion, the ith sx is given by,                               s          xi                ⁢                  xe2x80x83                ⁢                                            :=                        ⁢                          xe2x80x83                        [                                          Ln                ⁡                                  [                                                                                                              (                                                      λ                                                                                          i                                +                                1                                                            ,                              j                                                                                )                                                5                                            ·                                              W                        ⁡                                                  (                                                                                    λ                                                                                                i                                  +                                  1                                                                ,                                j                                                                                      ,                            T                                                    )                                                                                      -                                                                                            (                                                      λ                                                          i                              ,                              j                                                                                )                                                5                                            ·                                              W                        ⁡                                                  (                                                                                    λ                                                              i                                ,                                j                                                                                      ,                            T                                                    )                                                                                                      ]                                            +                                                a                  0                                                  (                                                            λ                                                                        i                          +                          1                                                ,                        j                                                              ⁢                                          T                                              i                        +                        1                                                                              )                                            -                                                a                  0                                                  (                                                            λ                                              i                        ,                        j                                                              ⁢                                          T                      i                                                        )                                                      ]                    ·                                    (                                                λ                                                            i                      +                      1                                        ,                    j                                                  -                                  λ                                      i                    ,                    j                                                              )                                      -                              1                xe2x80xa2                                                                        (        4        )            
sx is obtained by taking the average of sxi. Eqn. (1) can now be rewritten as,
Ln[W(xcex,T)xcex5/xcex1]xe2x88x92sx(T)(xcexxe2x88x92xcexL)=x0(T)xe2x88x92a0/(xcexT)xe2x80x83xe2x80x83(5)
T and x0 are determined by a least-squares best-fit of the RHS of Eqn. (5) to the LHS. This value of T is then used with Eqn. (1) to consistently determine the emissivity.
To minimize sensitivity to noise (from atmospheric absorptivity, electrical noise, etc.), standard signal preprocessing of the spectral intensity distribution measurements of time averaging and subtracting out background levels are performed at the beginning of this stage. Further preprocessing steps of discarding spectral regions having curvatures that are a factor of 10 or more greater than average, and discarding data from any of the spectral sub-regions yielding preliminary temperatures that are 10% or more different from neighboring sub-regions.
Two important differences between the Stage-1 method of the invention and the standard MW approach are that (1) a wide spectral range can be utilized with this approach to yield more accurate results with only a rough approximation of the emissivity, and (2) the spectral variation of the projected emissivity is determined independently of the temperature calculation.
The error in T can be estimated from the maximum change in the color temperature calculated from the various spectral sub-regions. The maximum and minimum temperatures obtained from this error estimate serve as input to Stage-2.
The Stage-2 temperature calculation is more accurate than that of Stage-1, but is computationally much more intensive, therefore, to ensure timely calculations, only a multiple of the temperature range obtained from the Stage-1 calculation is considered in Stage-2. The approach essentially compares at least two different spectral intensity distributions radiated at two different temperatures by the same source to obtain both temperatures. The different temperature spectra are acquired by imaging different surface areas of the source. It is important that the different spectral distributions be radiated with the same emissivity, and emissivity can be a function of temperature. But since its temperature dependence is much less than the temperature dependence of the intensity, and since the temperatures can be made arbitrarily close by imaging closely spaced surface regions of the source, the temperature dependence of the emissivity can be neglected.
First, spectral intensity measurements W(xcex,T) from at least two different temperature regions of the source are obtained. Correspondingly different projected emissivities xcex5xe2x80x2(xcex,T,Txe2x80x2) are then determined by dividing W(xcex,T) by the Plank blackbody intensity function evaluated at a projected source temperature Txe2x80x2. Since there is only one true spectral emissivity, which must be the same irrespective of the spectral intensity distribution used to calculate it, the correct two source temperatures are the two values of Txe2x80x2 that cause the corresponding two projected emissivity distributions to be equal. These two values of Txe2x80x2 can be determined by looking for the maximum correlation between the two normalized projected emissivities as a function of the projected temperatures. By definition, at these two values of Txe2x80x2, the projected emissivities both equal the true emissivity.
More explicitly, the correlation function approach can be summarized by the following. For two temperatures, Ta and Tb, the emissivity correlation function is defined as,                                less than                                     ϵ              h                        ⁡                          (                              λ                ,                                  T                  a                                ,                                  T                                      a                    xe2x80x2                                                              )                                      ,                  
                ⁢                                            ϵ              h                        ⁡                          (                              λ                ,                                  T                  b                                ,                                  T                                      b                    xe2x80x2                                                              )                                 greater than =                                    ∫                              λ                L                                            λ                U                                      ⁢                                                                                ϵ                    h                                    ⁡                                      (                                          λ                      ,                                              T                        a                                            ,                                              T                                                  a                          xe2x80x2                                                                                      )                                                  ·                                                      ϵ                    h                                    ⁡                                      (                                          λ                      ,                                              T                        b                                            ,                                              T                                                  b                          xe2x80x2                                                                                      )                                                              ⁢                              xe2x80x83                            ⁢                              ⅆ                λ                                                                        (        6        )            
where,             ϵ      h        ⁡          (              λ        ,        T        ,        T            )        :=                              ϵ          xe2x80x2                ⁡                  (                      λ            ,            T            ,                          T              xe2x80x2                                )                                      (                                    ∫                              λ                L                                            λ                U                                      ⁢                                                                                ϵ                    xe2x80x2                                    ⁡                                      (                                          λ                      ,                      T                      ,                                              T                        xe2x80x2                                                              )                                                  2                            ⁢                              xe2x80x83                            ⁢                              ⅆ                λ                                              )                .5              ⁢    xe2x80xa2  
and,             ϵ      xe2x80x2        ⁡          (              λ        ,        T        ,                  T          xe2x80x2                    )        :=                    W        ⁡                  (                      λ            ,            T                    )                                      W          B                ⁡                  (                      λ            ,                          T              xe2x80x2                                )                      ⁢    xe2x80xa2  
WB is the Plank blackbody intensity distribution function, and xcex5h is a normalized projected emissivity. The correlation between the two projected emissivities is determined by Eqn. (6), which attains a maximum value when Taxe2x80x2=Ta and Tbxe2x80x2=Tb. In addition, to facilitate the search for the maximum, Tb can be written in terms of Taxe2x80x2 as,       T          b      xe2x80x2        :=                    a        0            λ        ·                  [                  ln          ⁡                      [                                                            (                                                            e                                                                        a                          0                                                                          λ                          ·                                                      T                                                          a                              xe2x80x2                                                                                                                                            -                    1                                    )                                ·                                                      W                    ⁡                                          (                                              λ                        ,                                                  T                          a                                                                    )                                                                            W                    ⁡                                          (                                              λ                        ,                                                  T                          b                                                                    )                                                                                  +              1                        ]                          ]                    -                  1          xe2x80xa2                    
Stray-light contributions to the measured spectral intensity distribution that survived the initial preprocessing subtraction are conveniently determined and subtracted out within the calculation. A parameterized functional form of the residual stray-light contribution is subtracted from the measured spectral intensity distribution, and the difference is substituted for the measured distribution within the correlation function. For instance, if the main source of stray light are two incandescent bulbs operating at color temperatures of 2800 K and 3100 K, then the parameterized stray light function is,
C1WB(xcex, 2800K)+C2WB(xcex, 3100K), where C1 and C2 are the stray light parameters.
Then, in addition to finding the maximum correlation as a function of the projected source temperatures, the maximum is also determined as a function of the stray-light parameters. This maximum occurs when the values of the stray-light parameters accurately reflect reality. The result is accurate values for the source temperatures as well as for the stray light intensity distribution.
At this point, the emissivity determined from the Stage-1 or from the Stage-2 calculations is an effective spectral emissivity, which may be different from the true source spectral emissivity due to modification by atmospheric absorptivity via an extraneous multiplicative function. If the approximate spectral locations and relative magnitudes of the atmospheric absorption peaks are known and general material characteristics of the radiating source are known, parameterized functional forms for the source emissivity and for the atmospheric absorptivity (i.e. the extraneous function) can be assumed. The parameters are determined by equating the product of the two functional forms to the effective emissivity, and performing a best-fit calculation over the measured spectral range, thereby simultaneously computing the source spectral emissivity and the atmospheric absorption.
The measurement approach of the invention requires the near-simultaneous measurement of different intensity spectra, and is best accomplished with a multi-channel fiber-optic spectrophotometer with detector array configured with special optics, electronics, and computerized control (each channel is actually a separate spectrometer). Different surface areas and spectral regions of the radiation source are imaged onto the different spectrophotometer channels via computer-controlled auto-focus and auto zoom optical elements, and via waveguide cables. The auto-focus and auto-zoom allows simultaneous imaging of surface areas having a wide range of separation distances, which in turn yield the different temperature spectral intensity measurements required by the Stage-2 calculation. Additionally, the different spectral regions imaged provide a wide spectral coverage that enhances the accuracy of the Stage-1 and Stage-2 calculations. The preferred embodiment involves a total spectral width where the longest wavelength is greater than twice the shortest wavelength.